• Structural Engineering and Mechanics
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• v.45 no.5
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• pp.655-676
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• 2013

In this study, strength reduction factors and inelastic displacement ratios are investigated for SDOF systems with period range of 0.1-3.0 s considering soil structure interaction for earthquake motions recorded on soft soil. The effect of stiffness degradation on strength reduction factors and inelastic displacement ratios is investigated. The modified-Clough model is used to represent structures that exhibit significant stiffness degradation when subjected to reverse cyclic loading and the elastoplastic model is used to represent non-degrading structures. The effect of negative strain - hardening on the inelastic displacement and strength of structures is also investigated. Soil structure interacting systems are modeled and analyzed with effective period, effective damping and effective ductility values differing from fixed-base case. For inelastic time history analyses, Newmark method for step by step time integration was adapted in an in-house computer program. New equations are proposed for strength reduction factor and inelastic displacement ratio of interacting system as a function of structural period($\tilde{T}$, T) ductility (${\mu}$) and period lengthening ratio ($\tilde{T}$/T).

• Earthquakes and Structures
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• v.12 no.4
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• pp.397-407
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• 2017

To estimate the structural seismic demand, some methods are based on an equivalent linear system such as the Capacity Spectrum Method, the N2 method and the Equivalent Linearization method. Another category, widely investigated, is based on displacement correction such as the Displacement Coefficient Method and the Coefficient Method. Its basic concept consists in converting the elastic linear displacement of an equivalent Single Degree of Freedom system (SDOF) into a corresponding inelastic displacement. It relies on adequate modifying or reduction coefficient such as the inelastic deformation ratio which is usually developed for systems with known ductility factors ($C_{\mu}$) and ($C_R$) for known yield-strength reduction factor. The present paper proposes a rational approach which estimates this inelastic deformation ratio for SDOF bilinear systems by rigorous nonlinear analysis. It proposes a new inelastic deformation ratio which unifies and combines both $C_{\mu}$ and $C_R$ effects. It is defined by the ratio between the inelastic and elastic maximum lateral displacement demands. Three options are investigated in order to express the inelastic response spectra in terms of: ductility demand, yield strength reduction factor, and inelastic deformation ratio which depends on the period, the post-to-preyield stiffness ratio, the yield strength and the peak ground acceleration. This new inelastic deformation ratio ($C_{\eta}$) is describes the response spectra and is related to the capacity curve (pushover curve): normalized yield strength coefficient (${\eta}$), post-to-preyield stiffness ratio (${\alpha}$), natural period (T), peak ductility factor (${\mu}$), and the yield strength reduction factor ($R_y$). For illustrative purposes, instantaneous ductility demand and yield strength reduction factor for a SDOF system subject to various recorded motions (El-Centro 1940 (N/S), Boumerdes: Algeria 2003). The method accuracy is investigated and compared to classical formulations, for various hysteretic models and values of the normalized yield strength coefficient (${\eta}$), post-to-preyield stiffness ratio (${\alpha}$), and natural period (T). Though the ductility demand and yield strength reduction factor differ greatly for some given T and ${\eta}$ ranges, they remain take close when ${\eta}>1$, whereas they are equal to 1 for periods $T{\geq}1s$.

• Journal of the Earthquake Engineering Society of Korea
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• v.15 no.3
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• pp.11-26
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• 2011

The inelastic displacement ratio is defined as the ratio of the peak inelastic displacement to the peak linear elastic displacement. The inelastic displacement ratio allows simple evaluation of the peak inelastic displacement directly from the peak elastic displacement without computation of the inelastic response. Existing research of the inelastic displacement ratio is limited to piece-wise linear systems such as bilinear or stiffness degrading systems. In this paper, the inelastic displacement ratio is investigated for smooth hysteretic behavior systems subjected to near- and far-fault earthquakes. A simple formula of the inelastic displacement ratio is proposed by using a two step procedure of regression analysis.

• Journal of the Earthquake Engineering Society of Korea
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• v.11 no.6
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• pp.53-61
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• 2007

This study investigates the effect of site class, post-yield stiffness ratio, damping ratio, yield-strength reduction factor, and natural period on inelastic displacement ratio of bilinear SDF systems located at the sites classified as NEHRP site class B,C,D. The previous studies developed inelastic displacement ratio using equal displacement rule in the intermediate and long period range. But, this approximation overestimates the inelastic displacement ratio. Furthermore, inelastic displacement ratio has not been developed for the systems having a damping ratio less than 5%. This study conducts nonlinear regression analysis for proposing equations for calculating median and deviation of the inelastic displacement ratio of the bilinear SDOF system having damping ratios ranging from 0 to 20%. Using median and deviation of the inelastic displacement ratio, probabilistic inelastic displacement ratio is estimated, which can be used for performance-based seismic evaluation.

• Tunnel and Underground Space
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• v.9 no.3
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• pp.194-203
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• 1999

The axial stress in rock bolt, the shear stress at the bolt-grout interface and the neutral point are analyzed to understand the mechanical behavior of rook bolt. To analyze the support effects of rock bolt in various geological conditions, numerical analyses are performed with regard to bolt spacing and bolt length in several geological conditions and tunnel sizes. Through the numerical analyses, the distributions of maximum tensile stress and shear stress are determined. And the excavation width of underground opening affects the position of the neutral point. In the circular opening supported by pattern bolting, the increase of confining pressure, the reduction of plastic zone, and that of ground displacement are determined by using the radial stress increase ratio, the plastic zone reduction ratio and the displacement reduction ratio respectively. The results of this study can be applied to a practical tunnel design through understanding of the trends of these support effects.

• Structural Engineering and Mechanics
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• v.45 no.6
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• pp.741-758
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• 2013

In this study, inelastic displacement ratios are investigated for existing systems with known lateral strength considering soil structure interaction. For this purpose, SDOF systems for period range of 0.1-3.0 s with different hysteretic behaviors are considered for a number of 18 earthquake motions recorded on soft soil. The effect of stiffness degradation on inelastic displacement ratios is investigated. The Modified Clough model is used to represent structures that exhibit significant stiffness degradation when subjected to reverse cyclic loading and the elastoplastic model is used to represent non-degrading structures. Soil structure interaction analyses are conducted by means of equivalent fixed base model effective period, effective damping and effective ductility values differing from fixed-base case. For inelastic time history analyses, Newmark method for step by step time integration was adapted in an in-house computer program. A new equation is proposed for inelastic displacement ratio of system with SSI with elastoplastic or degrading behavior as a function of structural period ($\tilde{T}$), strength reduction factor (R) and period lengthening ratio ($\tilde{T}$/T). The proposed equation for $\tilde{C}_R$ which takes the soil-structure interaction into account should be useful in estimating the inelastic deformation of existing structures with known lateral strength.

• Structural Engineering and Mechanics
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• v.39 no.5
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• pp.683-701
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• 2011

In this study, inelastic displacement ratios and ductility demands are investigated for SDOF systems with period range of 0.1-3.0 s. with elastoplastic behavior considering soil structure interaction. Earthquake motions recorded on different site conditions such as rock, stiff soil, soft soil and very soft soil are used in analyses. Soil structure interacting systems are modeled with effective period, effective damping and effective ductility values differing from fixed-base case. For inelastic time history analyses, Newmark method for step by step time integration was adapted in an in-house computer program. Results are compared with those calculated for fixed-base case. A new equation is proposed for inelastic displacement ratio of interacting system ($\tilde{C}_R$) as a function of structural period of interacting system ($\tilde{T}$), strength reduction factor (R) and period lengthening ratio ($\tilde{T}/T$). The proposed equation for $\tilde{C}_R$ which takes the soil-structure interaction into account should be useful in estimating the inelastic deformation of existing structures with known lateral strength.

• Journal of Oral Medicine and Pain
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• v.23 no.1
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• pp.45-55
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• 1998

The author assessed the sagittal relationships between glenoid fossa of the temporal bone and mandibular condyle from lateral transcranial views of 74 TMJ with disc displacement and 16 TMJ with normal disc-condyle complex by the magnetic resonance image findings. All the subjects were female and also in their 3rd decades. The disc displacement group was subdivided into anterior disc displacement with reduction (ADWR) group and anterior disc displacement without reduction (ADWOR) group. The anterior, superior, and posterior joint spaces as well as anterior/posterior (A/P) ratio of the space at the closed jaw position and vertical and horizontal components of the condyle position relative to the articular eminence at the open jaw position were measured from all the subjects and the data were compared among groups. The result were as follows : 1. The mean posterior joint space of ADWR group was smaller than ADWOR group, but there were no significant differences in anterior and superior joint spaces between two groups. 2. There showed a tendency of higher A/P ratio in ADWR group which meant the condyle of ADWR was likely to take posteriorly displaced position. 3. There were higher proportion of neutral condylar position in glenoid fossa in normal group, but higher proportion of posterior condylar position in ADWR group. 4. There were no significant differences in the degree of condyle-fossa concentricity among groups.

• Journal of Industrial Technology
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• v.26 no.A
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• pp.153-161
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• 2006

The main objective of this study was to derive a formula of ductility reduction factor, expressed as $R_{\mu}$. To attain this objective, a study comprised reduction factors computed for stiffness degrading systems undergoing different levels of ductility and to investigate an accuracy of the formula. Based on this study, the main conclusions can be summarized :(1) The ductility reduction factor is primarily affected by the period of the system and the displacement ductility ratio. (2) The proposed formula is simpler and the inelastic deformations of bridge structures are better than those by the others formulas we used before.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 2007.04a
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• pp.777-782
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• 2007

Displacement amplification factor can be used to estimate inelastic displacement demands from elastic displacement demands, The simple formula for displacement amplification factor considering hysteretic behavior of structural system and earthquake characteristics is proposed. And the effects of several parameters such as displacement ductility, strain hardening ratio, period, characteristics of earthquakes and hysteretic models for the displacement amplification factor are evaluated. Accuracy of the proposed formula is evaluated by comparing the displacement amplification factors estimated by existing and proposed formula with those calculated from inelastic time history analysis. The displacement amplification factors by proposed formulas provide a good agreement with those calculated by inelastic time history analysis.